mapEdges

mapEdges is a concept used in graph theory and graph processing to describe a transformation that assigns to every edge in a graph a value from a chosen target set, or that otherwise replaces edge data. It is an edge-centric counterpart to vertex-focused mappings and is often used to derive new graphs or annotate existing ones with computed attributes.

Formally, let G = (V,E) be a graph and let f be a function that associates each edge e ∈ E with a value in a set X. Applying mapEdges to G with f yields a transformed object in which each edge carries the value f(e). Depending on the context, this may produce a new edge-labeled graph, alter edge weights, or define a new edge set.

Examples include creating a weighted graph by setting w'(e) = f(e) for all e, or generating a labeled graph where the label on e is f(e). In some frameworks, mapEdges can also map edges to new edges, effectively transforming the topology, though this is less common and requires careful handling to maintain vertex correspondences.

In software libraries, mapEdges is often implemented as a higher-order operation that takes a function parameter and returns a new graph with each edge data transformed accordingly. This is useful in pipelines that require edge-wise feature computation, normalization, or filtering without mutating the original graph.

See also mapVertices, graph transformation, edge labeling.